WASHINGTON (AP) — Emergency legislation to allow the government to borrow more money headed toward passage in the Senate Tuesday with just hours to spare before the national debt bumps against its ceiling. Expected approval sends the bill to President Barack Obama, averting a potentially disastrous, first-ever government default and making a down payment toward taming out-of-control budget deficits.

“Finally Washington is taking responsibility for spending money it doesn’t have,” Sen. Lamar Alexander, R-Tenn., said at the start of debate.

The legislation, which easily passed the House on Monday, is virtually assured to clear the Senate at midday noon by a bipartisan tally. The White House promises that Obama will quickly sign the measure into law. Obama planned to issue a statement after the vote.

The legislation pairs an increase in the government’s borrowing cap with promises of more than $2 trillion of budget cuts over the upcoming decade. Its passage caps a long, difficult battle between tea party-powered House Republicans and Obama — with House Speaker John Boehner caught in the middle more than once.

After months of fiercely partisan struggle, the House’s top Republican and Democratic leaders swung behind the bill, ratifying a deal sealed Sunday night with a phone call from Boehner to Obama.

“I’m not happy with it,” Minority Leader Nancy Pelosi, D-Calif., said. “But I’m proud of some of the accomplishments in it. That’s why I’m voting for it.”

Amid the high intrigue of the historic moment, the drama was heightened even further when Rep. Gabrielle Giffords, the Arizona congresswoman wounded in a shooting rampage seven months ago, made a surprise visit to the House floor to cast her vote. Colleagues on both sides of the aisle rushed to embrace her, and Pelosi publicly saluted her courage and resiliency.

Much of the House-passed measure was negotiated on terms set by Boehner, which included a demand that any increase in the nation’s borrowing cap be matched by spending cuts at least as large. But it also meets demands made by Obama, including debt increases large enough to keep the government funded into 2013 and curbs on growth of the Pentagon budget.

Even though Obama strongly supported the measure, half of the chamber’s Democrats opposed it. Sixty-six conservative Republicans opposed the measure as well.

Still, after storming the Capital in January — only to see bill after bill die in the Democratic Senate — many junior House lawmakers opted to view the legislation through the prism of optimism.

“It’s about time that Congress come together and figure out a way to live within our means,” said Rep. Sean Duffy, R-Wis. “This bill is going to start that process, although it doesn’t go far enough.”

The measure would provide an immediate $400 billion increase in the $14.3 trillion U.S. borrowing cap, with $500 billion more assured this fall. That $900 billion would be matched by cuts to agency budgets over the next 10 years.

What follows next is more complicated. The measure establishes a special bipartisan committee to draft legislation to find up to $1.5 trillion more in deficit cuts for a vote later this year. They’re likely to come from so-called mandatory programs like federal retirement benefits, farm subsidies, Medicare and Medicaid. The savings would be matched by a further increase in the borrowing cap.

There’s no guarantee the committee, to be evenly split between the warring parties, will agree on such legislation. But there are powerful incentives to do so because more budget gridlock would trigger a crippling round of automatic cuts across much of the budget, including Pentagon coffers.

And questions linger about the effect the grueling political free-for-all will have on the U.S. credit rating.

Treasury Secretary Timothy Geithner told ABC News in an interview that he didn’t know whether the debt-limit fight would cause America’s AAA credit rating to be downgraded. “It’s not my judgment to make,” he said. Geithner also said he fears world confidence in the United States was damaged by “this spectacle.”

The vote during Monday’s dinner hour in the capital came after intense efforts at persuasion by the administration.

The White House dispatched Vice President Joe Biden to the Capitol to lobby recalcitrant Democrats in both House and Senate. He heard an earful, especially from liberal and black lawmakers upset that Obama surrendered on taxes and agreed to cuts from a budget ledger built up over the first two years of his term, when Democrats dominated Congress.

“They expressed all their frustration,” he conceded after a session with House Democrats.

Biden said the deal “has one overwhelming redeeming feature” — postponing the next debt limit battle until 2013 and leaving the current fight behind. “We have to get this out of the way to get to the issue of growing the economy,” he said.

Rep. Jan Schakowsky, D-Ill., said the Republicans got the better of the deal.

“Republicans intentionally created a crisis in order to get their way,” Schakowsky said. “This is the wrong medicine for a sick economy. This bill could increase unemployment, slow economic growth and deepen already historic income inequality.”

GOP leaders lobbied their members as well, but with Democratic leaders and Obama behind the legislation, there was far less pressure on them than last week, when they were forced to delay a vote and rewrite an earlier version of the measure to assuage tea party lawmakers.

“This measure is not perfect or the way we would have done it if we were in charge, but it will finally begin to change the way Washington spends taxpayer dollars,” House Majority Leader Eric Cantor, R-Va., said. “As is the case with any major change, these things will take time and this is the first significant move — of many to come — to turn Washington around.”

In the Senate, support from Majority Leader Harry Reid, D-Nev., and GOP leader Mitch McConnell of Kentucky virtually guarantees the measure will receive the 60 votes required to pass on Tuesday. The vote is set for noon, plenty of time to ship the measure up Pennsylvania Avenue to Obama. The administration has said that without the new borrowing authority, the government won’t be able to pay all its bills after Tuesday.

Enactment of the measure would provide welcome closure for Obama, who has seen his poll numbers sag during the debt limit battle — especially as Tuesday’s deadline neared and the stock market sank.

GOP presidential candidates such as Mitt Romney and Michele Bachmann issued statements opposing the legislation.

“As with any compromise, the outcome is far from satisfying,” Obama conceded in a video his re-election campaign sent to millions of Democrats.

In a tweet, the president was more positive: “The debt agreement makes a significant down payment to reduce the deficit — finding savings in both defense and domestic spending.”